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Inv 6.3 Equilibrium of Forces and
Hooke’s Law
Investigation Key Question:
How do you predict the force on a spring?
6.3 Applications of equilibrium
If an object is not moving,
then you know it is in
equilibrium and the net
force must be zero.
You know the total upward
force from the cables must
equal the downward force of
the sign’s weight because
the sign is in equilibrium.
What is the upward
force in each cable?
6.3 Applications of equilibrium
Real objects can move in three directions: up-down, right-left, and front-back.
The three directions are called three dimensions and usually given the names x, y, and z.
When an object is in equilibrium, forces must balance separately in each of the x, y, and z dimensions.
6.3 The force from a spring
A spring is a device designed to
expand or contract, and thereby
make forces in a controlled way.
Springs are used in many devices
to create force.
There are springs holding up the
wheels in a car, springs to close
doors, and a spring in a toaster
that pops up the toast.
6.3 The force from a spring
The most common type of spring is a coil of
metal or plastic that creates a force when it is
extended (stretched) or compressed
(squeezed).
6.3 The force from a spring
The force from a spring has
two important
characteristics:
The force always acts in a
direction that tries to return
the spring to its
unstretched shape.
The strength of the force is
proportional to the amount
of extension or
compression in the spring.
6.3 Restoring force and Hooke’s Law
The force created by an extended or
compressed spring is called a
“restoring force” because it always
acts in a direction to restore the spring
to its natural length.
The change a natural, unstretched
length from extension or compression
is called deformation.
The relationship between the restoring
force and deformation of a spring is
given by the spring constant (k).
6.3 Restoring force and Hooke’s Law
The relationship between force, spring constant,
and deformation is called Hooke’s law.
The spring constant has units of newtons per
meter, abbreviated N/m.
6.3 Hooke's Law
The negative sign indicates that positive
deformation, or extension, creates a restoring
force in the opposite direction.
F = - k x
Spring constant N/m
Force (N)Deformation (m)
1. You are asked for force.
2. You are given k and x.
3. Use F = - kx
4. Substitute values: F = - (250 N/m)(0.01 m) F = - 2.5 N
Calculate the force from a spring
A spring with k = 250 N/m is extended
by one centimeter. How much force
does the spring exert?
6.3 More about action-reaction and normal
forces
The restoring force
from a wall is always
exactly equal and
opposite to the force
you apply, because it
is caused by the
deformation resulting
from the force you
apply.
1. You are asked for the deformation, x.
2. You are given force, F and spring constant, k.
3. Use F = - kx, so x = - F ÷ k
4. Substitute values: x = - (500 N/m) ÷ (1 × 108 N/m)
5. x = - 5 × 10-6 meters (a very small deformation)
Calculate the restoring force
The spring constant for a piece of solid wood is 1 × 108
N/m. Use Hooke’s law to calculate the
deformation when a force of 500 N (112 lbs) is applied.
We are surrounded by structures.
To design a structure well, you first need to know what forces
act and how, and where the forces are applied.
Engineering is the application of science to solving real-life
problems, such as designing a bridge.
The Design of Structures
An object on a spring is
pulled to the right of the
equilibrium position and
released from rest.
The diagram shows the
direction of the spring
force at five different
positions over the
course of the object's
path.
If we analyze the position vs time of the object, we
observe a sinusoidal variation.
This is called oscillatory or simple harmonic motion.
If we analyze the velocity vs time of the object, we observe again a
sinusoidal variation, with an offset of ¼ of the cycle.
Notice the speed is maximum at the equilibrium position, and zero at the
turning points.
One complete cycle is
called an oscillation
• The time it takes to complete one oscillation is
called the period P.
• The maximum displacement (positive or negative)
from equilibrium is called the amplitude
Equilibrium
position